To evaluate cost functions used in nearly all scientific disciplines around procedures. On basis of this evaluation then decisions can be made.

The economical cost function

The economical cost function summarizes all developing costs of a certain quantity of x of a product. Usually it contains of two components:

• the fixed costs
• and the variable costs.

K (x) = K_ {fixed} + K_ {var} \ cdot x

whereby with the variable costs every now and then also k instead of K is used and instead of the K_ {var} every now and then also only K_v. (in addition, k is used as unit cost prices, i.e. k = K/x)

Example

If one produces 10 cars, then first the fixed costs result, which develop independently of whether or how many cars (e.g. rent for the production hall) are produced. Further the variable costs are added, which develop for each produced car exactly once (e.g. per car costs of an engine).

Cost function in the complexity theory

The cost function in the complexity theory evaluates the run time behavior or the resources consumption of an algorithm. As cost function the so-called O-function is used (partly than land outer symbol, in the English big o notation designates mentioned).

o (f (x))= O (n^2)

Here distinctive according to increasing the complexity of a task with the increasing of the number of the input values.

Often becomes after constant (O (1)), linear (O (n)), square (O (n^2)), polynomialen (O (n^ {"…})) oderexponentiellem (O (e^n)) Behavior classifies.

Examples

If a person A eats an ice with 2 balls, needs her a time x. for an ice with 4 balls needs her the double time 2x. Thus we have a linear increase of processing (Ess) - time as a function of the quantity of the input. If another person B needs only half so long for 2 balls necessarily (x/2), then her for 4 balls a time x. we has the same linear increase as a function of the quantity of the ice balls. Thus we have a function ice meal with linear behavior (O (n)). Of course we ignore the dependence of speed of operation on the filling degree of the stomach in this simplified model.

If a program (for a Betriebwirtschaftler, which organizes an autofactory) maintains a list of cars, which are produced in the production hall, then the program can calculate the costs by the fact that it goes through the list and for each car an amount of constant K_ found in the list {var} added. The running time of this algorithm grows linear with list is however constantly related to the color of the cars in that list alternative can an algorithm the same computation implement, by determining the costs by unique multiplication K_ {var} \ cdot x. This algorithm is then constant in that running time, although the multiplication represents a more expensive operation in principle than the addition.

See also

Neighbouring costs, average costs, proceeds, proceeds function, collection of formulae economics

Articles in category "Cost function"

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